# Limiting absorption principle on Riemannian scattering (asymptotically conic) spaces, a Lagrangian approach

## TL;DR

This paper establishes the limiting absorption principle on asymptotically conic Riemannian spaces using a Lagrangian framework, demonstrating Fredholm properties of spectral families in specialized function spaces.

## Contribution

It introduces a Lagrangian approach to prove the limiting absorption principle on asymptotically conic spaces, extending scattering theory techniques.

## Key findings

- Spectral family is Fredholm in Lagrangian-regularity spaces
- Results hold for non-zero spectral parameters on and off the spectrum
- Persistence of properties in the physical half plane

## Abstract

We use a Lagrangian perspective to show the limiting absorption principle on Riemannian scattering, i.e. asymptotically conic, spaces, and their generalizations. More precisely we show that, for non-zero spectral parameter, the `on spectrum', as well as the `off-spectrum', spectral family is Fredholm in function spaces which encode the Lagrangian regularity of generalizations of `outgoing spherical waves' of scattering theory, and indeed this persists in the `physical half plane'.